Vision Research 40 (2000) 3475 – 3483
www.elsevier.com/locate/visres
Illusory contour strength does not depend on the dynamics or
relative phase of the inducers
Jonathan D. Victor *, Mary M. Conte
Department of Neurology and Neuroscience, Weill Medical College of Cornell Uni6ersity, 1300 York A6enue, New York, NY 10021, USA
Received 4 January 2000; received in revised form 26 June 2000
Abstract
We use a new objective measure of illusory contour strength, threshold reduction for aspect ratio discrimination, to examine
the effect of dynamics and relative phase on the Kanizsa illusion. We found no dependence of illusory contour strength on the
relative phase of flickering inducers (in phase, antiphase, or in quadrature phase) either for the standard Kanizsa square, or for
modifications that facilitated or interfered with amodal completion. Comparison with a vernier acuity task indicates that the
distance between the inducers, rather than the nature of the task, accounts for the insensitivity to relative phase. © 2000 Published
by Elsevier Science Ltd.
Keywords: Illusory contours; Hyperacuity; Temporal phase
1. Introduction
Illusory contour formation (Kanizsa, 1976; Prazdny,
1985) and hyperacuity judgments (Westheimer, 1981;
Klein & Levi, 1985) highlight the great spatial specificity with which visual inputs can be combined. Vernier
alignment thresholds are elevated for static targets
whose components have opposite polarity (Mather &
Morgan, 1986; Levi & Westheimer, 1987; O’Shea &
Mitchell, 1990) compared with targets whose components have like polarity. Such stimuli may be considered the low-frequency limit of antiphase and in phase
flickering stimuli. For vernier targets with flickering
components, relative phase indeed has a dramatic effect
on alignment thresholds (Victor & Conte, 1999), most
prominently below 4 Hz.
However, it is unclear whether relative phase has an
analogous effect on illusory contour formation. Initial
studies based on a subjective measure of illusory contour strength (Shapley & Gordon, 1983, 1985; Grossberg & Mingolla, 1985) found no effect of the relative
polarity of the inducers, while later studies, based on a
formal rating scale or saliency in a search task, found a
* Corresponding author. Tel.: +1-212-7462343; fax: + 1-2127468984.
E-mail address: jdvicto@med.cornell.edu (J.D. Victor).
diminution in strength with opposite-polarity inducers
(Matthews & Welch, 1997; Spehar, 1998; He & Ooi,
1998a,b). For stimuli with dynamic inducers, a study
based on comparison of synchronous and asynchronous alternatives found no effect of component
dynamics (Fahle & Koch, 1995), while one based on
adjustment and rating (Kojo, Liinasuo, & Rovamo,
1993) found a modest effect.
In this study, we re-examine the effect of stimulus
dynamics on illusory contour strength. We concentrate
on the frequency range and relative phases in which the
effect of dynamics on vernier alignment (Victor &
Conte, 1999) is most marked (1–4 Hz). We use a
readily quantified measure of illusory contour strength,
that is objective and demonstrably graded, albeit indirect. With this approach, we find no effect of component asynchrony on illusory contour strength for
flickering stimuli. We also show that a simple modification of the vernier stimulus, namely, introduction of a
gap between components, eliminates the effect of relative phase on alignment thresholds. This demonstrates
that the differences in dynamics of vernier alignment
and illusory contour formation depend on the spatial
separation of the stimulus components, rather than on
the nature of the task (e.g. binding vs. alignment, or
all-or-none vs. graded).
0042-6989/00/$ - see front matter © 2000 Published by Elsevier Science Ltd.
PII: S 0 0 4 2 - 6 9 8 9 ( 0 0 ) 0 0 1 9 0 - 5
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J.D. Victor, M.M. Conte / Vision Research 40 (2000) 3475–3483
2. Methods
2.3. Illusory contour stimuli
2.1. Subjects
The basic Kanizsa (1976, 1979) square stimulus had a
contrast of 0.50, an edge length L=3 deg, and an
inducer radius R=0.75 deg, yielding a support ratio
([real contour length]/[edge length]= 2R/L) of 0.5. Displays consisted of the inducer tokens of a Kanizsa
square, slightly displaced to create an illusory rectangle.
Subjects judged whether this rectangle was in a ‘portrait’ or ‘landscape’ orientation. We determined the
threshold aspect ratio for this shape judgment in the
standard Kanizsa configuration (in which the inducers
were rotated inward, permitting the formation of an
illusory contour), and for a configuration in which the
inducers were rotated outward (preventing the formation of the illusory contour). In both cases, the inducers
were presented with luminance polarities that were in
phase or antiphase. These four combinations are shown
in Fig. 1A. As explained below, our index S for the
strength of the illusory contour is the reduction in the
threshold log aspect ratio for shape discrimination
when a potential illusory contour is present (ln rin),
compared with when it is absent (ln rout), i.e. S=
(ln rout)/(ln rin). S= 1 corresponds to no measurable
Studies were conducted in three male and six female
normal subjects, ranging in age from 20 to 45. Three
experienced psychophysical subjects (MC, EM, YLF)
participated in all experiments and at least one naive
observer participated in Experiments 1 – 3. All subjects
had visual acuities (corrected if necessary) of 20/20 or
better.
2.2. Display
These visual stimuli were produced on a Sony Multiscan 17seII monitor, with signals driven by a PC-controlled Cambridge Research VSG2/3 graphics
processor. The resulting 768× 1024 pixel display had a
mean luminance of 47.2 cd/m2, a refresh rate of 100 Hz,
and subtended 6.4 × 8.6 deg (0.5 min per pixel) at the
viewing distance of 200 cm. The intensity versus voltage
behavior of the monitor was linearized by photometry
and lookup table adjustments provided by VSG
software.
Fig. 1. (A) Illusory contour stimuli. From top to bottom, inducers presented in phase rotated out, antiphase rotated out, in phase rotated in,
antiphase rotated in. (B) Mean threshold log aspect ratios ln rout (circles) and ln rin (squares) for shape discrimination with inducers presented in
phase (open symbols), and in antiphase (filled symbols). Error bars represent 9 2 S.E.M., calculated across subjects’ individual means of ln rin and
ln rout. (C) Illusion strength S = (ln rout)/(ln rin) derived from data of panel B. Open circles, inducers in phase; filled circles, inducers in antiphase.
Error bars represent 92 S.E.M., calculated across subjects’ individual measures of S. Support ratio 0.5, contrast 0.5. N = 7.
J.D. Victor, M.M. Conte / Vision Research 40 (2000) 3475–3483
effect of the putative illusory contour; values of S\ 1
correspond to progressively stronger effect of the
contour.
2.4. Vernier stimuli
Stimuli consisted of two horizontal bars (0.5 – 2 deg
long), with or without a horizontal gap. Bars had a
Gaussian profile (full width at half maximum 0.125 deg).
Subpixel vertical displacements d were produced by
shifting the Gaussian bar profiles pixel by pixel
(Krauskopf & Farell, 1991; Victor & Conte, 1999).
3477
For vernier experiments, each trial consisted of a single
stimulus interval containing a standard vernier bar pair,
with one of the horizontal bars displaced by an amount
d. The subject was asked to indicate which bar was
displaced upward. Bar positions were jittered as above
to eliminate the use of the borders of the display as an
absolute positional cue.
Unless otherwise noted, statistical comparisons between conditions were based on one-tailed paired t-tests
across subjects, without correction for multiple
comparisons.
2.5. Psychophysical methods
3. Results
Stimuli were presented for 1 s, under an envelope that
ramped on and off over 30 ms at onset and offset (Victor
& Conte, 1999). Staircases consisted of two preliminary
reversals in which the parameter of interest (log aspect
ratio ln r or displacement d) was changed by 0.3 log units,
followed by ten reversals with a step size of 0.1 log units.
The threshold estimate from each staircase was the
geometric mean of eight reversals (the final ten reversals
with one high and one low outlier excluded). The
parameter value was decreased following two successive
correct judgments, and increased by the same factor
following each incorrect judgment, providing an estimate
of the parameter required for 71%-correct judgments.
Five (Experiment 1) or six (Experiments 2 – 4) staircases
were combined (geometric mean) to obtain each subject’s
threshold for each condition. Within each experiment,
staircases for the several conditions were interleaved and
counterbalanced within and across subjects. Brief practice sessions sufficed to attain stable performance. Trials
were self-paced, and organized into sessions of 20–36
staircases, lasting 1– 2 h. The typical staircase contained
50 – 60 judgments.
For illusory contour experiments, each trial consisted
of two successively-presented stimulus intervals (500 ms
interstimulus interval) with aspect ratios differing by a
factor of r, one in ‘portrait’ orientation (V:H= r 1/2), and
the other in ‘landscape’ orientation (V:H=r − 1/2). The
subject was asked to identify which interval contained the
figure that was closer to a ‘landscape’ orientation. This
two-interval approach was used to avoid erroneous
judgments due to subtle geometrical distortions of the
display or observer bias. The position of the stimuli
relative to the center of the display was jittered from
trial-to-trial (15% of side length L) to prevent the use of
the edge of the frame as a cue to position or shape. To
avoid the use of unintended spatial cues such as the
absolute or relative sizes of the gaps, the nominal side
length L of the illusory square was jittered from trial-totrial (15% of side length L) and the radii of the inducers
R were independently jittered from trial-to-trial (10% of
side length L).
3.1. Experiment 1: dependence of illusory contour
strength on inducer dynamics
Fig. 1B shows aspect ratio thresholds for static inducers and flickering inducers presented at 1, 4, and 16 Hz.
For inwardly-rotated inducers, the mean threshold log
aspect ratio ln rin was 0.01–0.02 (Fig. 1B, filled circles).
For outwardly rotated inducers, the mean threshold log
aspect ratio ln rout was 0.03–0.04 (Fig. 1B, open circles).
This increase in aspect ratio threshold, consistent with
the observations of Regan and Hamstra (1992), indicated
that shape discrimination improved when an illusory
contour was present, compared with performance on a
similar task in which illusory contours were absent.
When the phase of one pair of diagonally-opposing
inducers was reversed, the log aspect ratio thresholds at
1, 4, and 16 Hz were unchanged (P\0.19 for ln rin and
ln rout at the three flicker frequencies) across the individual subjects (N= 7). However, for static stimuli, this
phase reversal caused a slight but statistically significant
(P= 0.035) increase in log aspect ratio ln rin compared
with the in phase condition.
The ratio S=ln rout/ln rin expresses the improvement
in aspect ratio threshold when illusory contours are
present, and is therefore taken to be a measure of their
strength. This ratio was 2.5–3 (Fig. 1C) for flickering
inducers at the three temporal frequencies studied, for
both in phase (open circles) and antiphase (filled circles)
conditions. However, for static inducers, there is a small
(30%) but significant decrease in illusion strength for the
antiphase condition compared with the in phase condition (P= 0.022).
We also examined the effect of ‘quadrature phase’
modulation, a condition in which the phase of one pair
of diagonally opposing inducers was shifted by a quarter
of a cycle, rather than half a cycle as in the antiphase
condition. With antiphase modulation, the luminances of
the inducers are asynchronous, but the instants of
contrast reversal remain synchronous. Synchronous contrast reversal, even if opposite in phase, may facilitate
grouping under some circumstances (Lee & Blake, 1999).
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Fig. 2. Illusion strength S= (ln rout)/(ln rin) at a range of support ratios, for inducers in phase (open symbols) or antiphase (solid symbols), at four
flicker frequencies. Geometric means across four subjects.
But with quadrature phase modulation, the instants of
contrast reversal are maximally separated in time. This
quadrature phase condition also has an anomalously
large effect on vernier acuity thresholds (Victor & Conte,
1999). At a flicker frequency of 4 Hz, the log aspect ratio
thresholds (ln rin, ln rout) and their ratio S=ln rout/ln rin
for the quadrature phase conditions (data not shown)
were not statistically different from their values in the in
phase and antiphase conditions (P \ 0.1 within each of
three subjects for both ln rin and ln rout by unpaired
t-test, P\0.2 across subjects for S by paired t-test).
3.2. Experiment 2: dependence on support ratio
To rule out the possibility that our measure S was
insensitive to a graded change in illusory contour
strength, we examined the dependence of S on support
ratio (Fig. 2). At a support ratio of 0.2, S was close to
1, and, as in the data of Fig. 1C, S was in the range 2.5–3
at a support ratio of 0.5. For the intermediate support
ratio 0.3, intermediate values of S (1.5 – 2) were obtained,
both in the group means as illustrated, and in the data
from each subject. The slight decrease in illusion strength
for the antiphase condition at 0 Hz with a support ratio
of 0.5 reproduces the findings in Fig. 1. At 16 Hz, there
was an increase in illusion strength S = ln rout/ln rin for
the antiphase condition, and reflected the behavior of a
single subject (LC), who showed both a modest decrease
in rin and a comparable increase in rout under these
conditions. Across the 12 conditions (four frequencies,
three support ratios), none of the differences between the
in phase and antiphase conditions were statistically
significant (P \0.05). In sum, Fig. 2 demonstrates that
our assay provides a graded measure of illusory contour
strength and that gradations in strength do exist, but
(within the parameter range we studied), these gradations do not depend on the relative phase of the inducers.
3.3. Experiment 3: dependence on perceptual
organization
Previous studies (Matthews & Welch, 1997; Spehar,
1998; He & Ooi, 1998a,b), found perceptual differences
of illusory contours that depended on the polarity of the
inducers. These studies differed from ours both in the
design of the stimuli and in the approach to assay
illusory contour strength (magnitude estimation or
search reaction time). We next examined whether differences in stimuli might account for the differences in
results.
Fig. 3A and B demonstrate the effects of altering
the standard Kanizsa square along the lines suggested
by the ‘Illusory O’ of He & Ooi (1998a,b). As
demonstrated by these authors, if the wedges are of
matching polarity to their associated inducers, amodal
completion of an occluding square frame is facilitated
(Fig. 3A), whether adjacent inducers are in phase
or in antiphase. If the wedges and the associated
inducers are of opposite polarity (Fig. 3B, ‘mismatch’
conditions), amodal completion of the occluding
square is reduced. The corresponding scene interpretation of occluded but non-uniform disks would
J.D. Victor, M.M. Conte / Vision Research 40 (2000) 3475–3483
require a non-generic scene interpretation (Nakayama
& Shimojo, 1992) in which the occluder ‘accidentally’
occludes just the portion of the disks in which luminance contrast changed. However, despite this difference in perceptual organization, we found no difference
between aspect ratio thresholds rin in these four conditions, for either static or flickering (1, 4, and 16 Hz)
conditions (P\ 0.05).
Spehar (1998, 1999) demonstrated that shape discrimination of a closed contour was impaired when
contrast reversals occurred along its edges, but not
when these reversals occurred at the corners. To determine whether such reversals had an effect on our assay
of contour strength, we modified the stimuli as shown
in Fig. 3C. We used sector angles of 120 and 150 deg,
rather than 135 deg, lest the alignment of the partitions
along the diagonal provide another cue to aspect ratio.
In phase and antiphase configurations both had contrast reversals at the corners, but only the in phase
configuration had a contrast reversal along the illusory
edge. Thus, according to Spehar’s results, perceptual
closure of the squares might be facilitated in the an-
3479
tiphase condition. However, as seen in Fig. 3C,
threshold log aspect ratios ln rin were unaffected (P\
0.05) by relative phase, and very similar to those measured in other configurations with a support ratio of 0.5
(Fig. 1B, Fig. 2 and Fig. 3A and B).
3.4. Experiment 4: spatial separation and dynamics in
a 6ernier task
The final experiment examines the effect of a gap
between stimulus components in a vernier alignment
task for which there is a striking effect of relative phase
when no gap is present (Victor & Conte, 1999). Bar
stimuli (0.5× 0.125 deg) were modulated at 2 Hz, near
the peak of the phase effect previously reported for
abutting bars (gap of 0 deg). The effects of this manipulation are shown in Fig. 4 at two contrasts, for an
individual subject (Fig. 4A) and a mean of three subjects (Fig. 4B). In the no-gap condition, we reproduced
our previous findings of an approximately threefold
improvement in vernier thresholds in the in phase condition, compared with the threshold in the antiphase
Fig. 3. Mean threshold log aspect ratios ln rin for shape discrimination of illusory squares, with inducers modified by an additional wedge that
is matched (A) or mismatched (B) in contrast polarity. Panel C, mean threshold log aspect ratios ln rin with inducers modified by contrast reversal
across an internal contour. In each case, inducers were presented in phase (left diagrammed stimulus, open circles) and antiphase (right
diagrammed stimulus, filled circles). Error bars as in Fig. 1B. N =5 (A, B); N= 6 (C).
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J.D. Victor, M.M. Conte / Vision Research 40 (2000) 3475–3483
Fig. 4. Dependence of displacement threshold on gap size. Vernier bars were 0.5 ×0.125 deg, and flickered at 2 Hz. (A) Displacement thresholds
for bars presented in phase (open circles) and antiphase (filled circles), at two contrasts. Error bars in Panel A represent 9 2 S.E.M., calculated
from the subject’s repeated staircase determinations for each condition. Subject MC. (B) Ratios of displacement threshold (antiphase/in phase) for
three subjects. Data from the subject of panel A are plotted with circles.
condition. This improvement is comparable to the improvement seen for static stimuli (Mather & Morgan,
1986; Levi & Westheimer, 1987; O’Shea & Mitchell,
1990). But with even a small gap (0.125 deg in this
subject), the difference between in phase and antiphase
presentation is lost. The effect of the gap was to
elevate the threshold for the in phase condition, rather
than to decrease the threshold for the antiphase condition. This is consistent with the notion that there is a
special mechanism recruited for the abutting vernier
task in the in phase condition, but not with the
notion that antiphase presentation interferes with judgment of alignment. Small gaps sufficed to equate the
thresholds for the in phase and the antiphase condition,
a gap of 0.125 deg in two subjects, and a gap of 0.25
deg in the third subject (Fig. 4B). These findings were
consistent across contrasts (c =0.2 and c= 0.8, as
shown).
Similar results were found for stimuli scaled up
by a factor of two (1.0× 0.25 deg bars with 0.25
deg gap) and four (2.0 ×0.5 deg bars with 0.5 deg
gap) in spatial extent. All threshold ratios (antiphase/in
phase) were not significantly different from 1 via
paired t-tests. Thus, the loss of sensitivity to
relative phase seen with the larger gaps depends on the
absolute size of the gap, rather than its size relative to
the bar.
4. Discussion
4.1. Summary of results and comparison with pre6ious
studies
We used a quantitative and demonstrably graded
(Fig. 2) measure of illusory contour strength to look for
effects of the relative phase of inducers on the strength
of the illusory contours that define a Kanizsa square.
We found no effect of phase on the strength of the
illusory contours over a range of flicker frequencies
from 1 to 16 Hz, either with standard Kanizsa squares
(Figs. 1 and 2) or with modifications designed to alter
the ways in which the illusory squares could be perceived (Fig. 3). For flickering inducers, these findings
extend a previous study of the effects of inducer asynchrony (Fahle & Koch, 1995) to a lower frequency
range. For static inducers of opposite polarity, an illusory contour is present (Shapley & Gordon, 1983, 1985,
1987; Grossberg & Mingolla, 1985), but our quantitative measures show that it is reduced in strength, consistent with recent studies based on a formal rating
scale or saliency in a search task (Matthews & Welch,
1997; He & Ooi, 1998a,b; Spehar, 1998, 1999).
He and Ooi (1998a,b) suggest that the illusory contour percept is related to a perceptual organization of
the Kanizsa square stimulus into two depth planes,
J.D. Victor, M.M. Conte / Vision Research 40 (2000) 3475–3483
with the illusory square seen as an opaque object that
partially occludes four disks. The completion of the
illusory square is considered to be ‘amodal’, since it does
not differ from the background along any modality. A
similar interpretation of other novel illusory contours
was recently advanced by Williams and Rubin (1998).
This amodal completion of the contour between inducers
(for example Figure 2 and Figure 3 of He & Ooi, (1998b)
and our Fig. 1) would account for a lack of dependence
of the contour strength on inducer polarity, since the
occluding square would be just as vivid, whether it
occluded like-contrast disks (in phase condition) or
opposite-contrast disks (antiphase condition). In further
support of this notion, He and Ooi (1998a,b) introduced
variations of the Kanizsa square (the ‘Illusory O’), in
which inducer polarity influenced whether scene organization was consistent with an unseen occluding object
(Figure 4 of He & Ooi (1998b)). Under static conditions,
their rating-scale measures indicated a strong dependence
of the strength of the illusory contours on the contrast
polarity of the inducers.
Our findings differ, in that we found no difference in
illusory contour strength for comparable variations of
the Kanizsa square, either under static conditions, or
when the inducers were modulated in antiphase. While
there is an apparent subjective difference in the saliency
of the squares due to these manipulations, there is no
degradation in shape discrimination (Fig. 3A and B). As
shown in Fig. 2, if there were a difference in illusion
strength comparable to a 25% reduction of the support
ratio, then our procedures would have been able to detect
it. In the rating-scale approach, the basis for the subjects’
judgments is uncertain — but it is reasonable that the
judgment criterion is shaped by the stimuli used for
training: exemplars in which the inducers are in phase.
Another possibility is that subjects made use of an
induced brightness illusion across the illusory contour
(Dresp & Bonnet, 1991). An illusory brightness difference would have been ambiguous or eliminated (Dresp,
Salvano-Pardieu, & Bonnet, 1996) in the antiphase
(opposite-polarity) condition. The most interesting possibility for the discrepancy in results is that there is a
distinction between a low-level process that extracts
contours, and a higher-level process that extracts scene
organization (Nakayama & Shimojo, 1992). This is
suggested both by inspection of the examples in Fig. 3
and the interpretation of He and Ooi (1998b), and would
account for the absence of polarity effects in our task but
not in those that are weighted by overall scene organization (He & Ooi, 1998a,b; Spehar, 1998, 1999).
The task we used relies on neither the use of exemplars
nor perceived brightness differences, but just on the
finding (Regan & Hamstra, 1992) that aspect ratio
discrimination for a rectangular object is several fold
better than discrimination of relative distances of isolated
pairs of points. The ability to perceive small changes in
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the geometry of the illusory object requires the presence
of the illusory contours for two-dimensional (Rubin,
Shapley, & Nakayama, 1995; Ringach & Shapley, 1996)
and three-dimensional (Carman & Welch, 1992) curvature judgments. We suspect that had we used one of these
other shape tasks (for example, by comparing thresholds
for thin vs. thick judgments Rubin et al. (1995) as a
function of relative phase), the results would have been
similar to what we found with the aspect ratio task.
4.2. Comparison with 6ernier alignment
Vernier judgments and illusory contour formation are
both early stages of visual analysis in which elementary
stimulus components are processed jointly, and the
extent to which these components are grouped is strongly
dependent on their relative geometry. As such, both
processes represent an early stage of the ‘binding’ of
stimulus components into a composite (Fahle & Koch,
1995), i.e. object extraction. The lack of dependence of
illusory contour strength on relative contrast polarity or
phase of the inducers differs from the well-known characteristics of vernier alignment. Vernier alignment
thresholds for static stimuli are several times lower for
stimulus components of like contrast polarity (Mather &
Morgan, 1986; Levi & Westheimer, 1987; O’Shea &
Mitchell, 1990), and alignment thresholds for flickering
stimuli are two to three times lower for stimuli whose
components are in phase than for stimuli whose components are out of phase (Victor & Conte, 1999).
Illusory contour formation and vernier acuity share a
precise dependence on spatial arrangement, but there are
also obvious differences between these two processes.
Vernier acuity can be demonstrated with stimuli that are
nearly confined to a single orientation, but illusory
contour stimuli necessarily involve the interaction of two
(or more) orientations. Although introduction of spatial
offsets generally interferes markedly with the strength of
the illusory contour (Fahle & Koch, 1995), other spatial
manipulations have modulatory effects — such as altering the perceived curvature and three-dimensional structure of a surface (Carman & Welch, 1992) or its
brightness (Grossberg & Mingolla, 1985). Illusory contour formation has been shown to be affected by ‘top–
down’ influences of scene organization (Lesher &
Mingolla, 1993; Ramachandran, Ruskin, Cobb, RogersRamachandran, & Tyler, 1994; He & Ooi, 1998a,b;
Spehar, 1998, 1999).
Nevertheless, it appears that separation of the stimulus
components, rather than these other factors, underlies
the differential effect of relative phase in these two tasks.
As shown in Fig. 4, insertion of a small gap into the
vernier stimulus eliminates the effect of relative phase.
The Kanizsa square configuration is incompatible with
the converse experiment, since eliminating the gap (support ratio equal to 1) replaces the space for the
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J.D. Victor, M.M. Conte / Vision Research 40 (2000) 3475–3483
illusory contour by a real contour. Moreover, our
approach cannot be used for support ratios close to 1,
since the length of the gap would be a strong confound
in the shape judgment task. Thus, we cannot directly
determine whether closing the gap will allow for the
emergence of temporal effects. However, experiments
based on another illusory contour stimulus, offset gratings, have shown a contrast polarity effect for abutting
stimuli (Dresp et al., 1996).
By demonstrating a common pattern of dependence
on relative temporal phase and separation, our analysis
expands the relevance of the short-range versus longrange dichotomy that characterizes performance in
vernier and other (Levi, Jiang, & Klein, 1990) hyperacuity tasks (reviewed in Victor & Conte, 1999) to tasks
involving extended contours (Dresp, 1999; Dresp &
Grossberg, 1997). In the short-range regime (Klein &
Levi, 1985; Wilson, 1986), contrast and temporal effects
on vernier and related tasks are prominent, consistent
with the notion that tuning properties of individual
neurons with quasilinear receptive fields play a limiting
role in performance (Shapley & Victor, 1986; Swindale,
1995). In the long-range regime, contrast and temporal
effects are weak or absent, and performance appears to
be limited by positional uncertainty (Burbeck, 1987;
Morgan, Ward, & Hole, 1990; Kooi, DeValois, &
Switkes, 1991; Levi & Waugh, 1996) of tokens extracted at an earlier stage of processing. The stage of
token extraction is presumably mediated by neurons
that can be modeled in a quasilinear fashion, followed
by a local non linearity. The second stage of analysis, at
which these tokens are jointly analyzed, follows the
local non linearity (Levi & Waugh, 1996), and thus is
insensitive to the internal detail of the tokens, including
temporal composition as shown here, and spatial frequency composition (Dakin & Hess, 1998). Successful
computational models for illusory contours (Heitger,
Rosenthaler, von der Heydt, Peterhans, & Kubler,
1992; Gove, Grossberg, & Mingolla, 1995) and related
grouping phenomena (Gove et al., 1995Grossberg,
Mingolla, & Ross, 1997; Yen & Finkel, 1998) share
these main features of local feature extraction (requiring a local non-linearity) followed by a long-range (also
non-linear) interaction. Moreover, this picture is consistent with the major architectural features of V1 and V2
(Spitzer & Hochstein, 1985; Ts’o, Gilbert, & Wiesel,
1986Heitger et al., 1992 Gilbert, Das, Ito, Kapadia, &
Westheimer, 1996).
Acknowledgements
We thank Rahil Rahim and Jeremy Perlman for their
assistance. A portion of this work was presented at the
1998 meeting of the Association for Research in Vision
and Ophthalmology in Ft. Lauderdale, FL (Victor &
Conte, 1998). This work was supported by NIH grant
EY7977.
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